BMSAT Kozhikode 2026

An apartment association lets its members pay 11 months of their monthly maintenance fee in lumpsum, while the usual option of monthly payments also exists. The treasurer claims that placing the 11-month lumpsum in a bank fixed deposit yields the same sum as 12 months of regular payment, as assessed at the year-end (assuming the monthly payments are not reinvested by the treasurer). What's the fixed deposit's rate of interest?

The average marks in Maths exam of students in group A, group B and both the groups together are 80, 90 and 87 respectively. Which of the following cannot be the total number of students in the two groups?

If $2^x/(1 + 2^x) = 1/3$, then $8^x/(1-8^x) = ?$

An examination consists of 160 questions. One mark is given for every correct option. If a 1/4 mark is deducted for each wrong option and a half mark is deducted for each unanswered question, then a student scores 79. If half a mark is deducted for every wrong option and 1/4 mark is deducted for every unanswered question, the same student scores 76. Find the number of correct answers he wrote.

Runs scored by Sachin in a charity match are 10 more than the balls faced by Lara. The number of balls faced by Sachin is 5 less than the runs scored by Lara. Together, they have scored 105 runs and Sachin faced 10 balls less than the balls faced by Lara. How many runs were scored by Sachin?

Integer multiples of 3 are arranged in increasing order, starting with 3, such that the difference between $k^{th}$ number in this list and $(k+1)^{th}$ is the LCM of 3 and $k$. Calculate the sum of the first 5 numbers.

In a $\triangle ABC$, D is a point on AC such that AD=2 cm, DC = 6 cm and $\angle ADB = \angle ABC$. Which of the following cannot be the length of BC?

Suppose the tax rules allow a person to either pay 20% of their total annual income as income tax, or pay 25% after claiming a deduction of Rs 2 lakh from the total annual income. What is the lowest annual income above which the former regime is attractive to the taxpayer?

A painting contractor tells the owner of a large custom-built cupboard that the painting cost will be proportional to the square of a cupboard's surface area as measured in square-m. The owner dismantles the cupboard into 4 modules in the ratio 3:5:6:8 of its surface area, such that no new surfaces are required to be painted. If the owner's savings turn out to be Rs 1400 due to the dismantling, what was original painting cost quoted by the contractor?

The sides of a triangle are 2006 cm, 6002 cm and 'm' cm, where m is a positive integer. How many values of 'm' are possible?

The product of 3 integers A, B, and C is 4096. The geometric mean of B and C is 32, whilst that of A and B is 8. Calculate C.

Each seat of first class, business class and economy class in an airplane occupies carpet area on the airplane's floor in ratio 4:2:1. The number of these seats in the airplane are in the ratio 1:2:8. Suppose that all the tickets in a class are offered at the same price, and these prices follow the former ratio. What is the contribution of the economy class to the airplane's revenue on a flight?

If $\sin\theta$ and $\cos\theta$ are the roots of the quadratic equation $px^2+qx+r=0$ $(p \neq 0)$, then which of the following relation holds good?

The area of the triangle formed by the lines $y = 4$, $x/5 + y/4 = 1$ and $x/5 - y/8 = 1$ is

In the given figure, two concentric circles with centre O have radii 14 cms and 7 cms. If $\angle AOB = 30^{\circ}$, find the area of the shaded region.

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If $\log_6 x + 2\log_{36} x + 3\log_{216} x = 9$, then $x =$ ___

If $a = \sqrt{11} - \sqrt{10}$, $b = \sqrt{12} - \sqrt{11}$, and $c = \sqrt{13} - \sqrt{12}$, then which of the following is true?

A sphere fits exactly in a hollow cube. Find the ratio of the volumes of the cube and the sphere

If $a^p = b^q = c^r = abc$, then $pqr = ?$

If $2^{n+m}/(2^{n-m}) = 16$ and $a = 2^{1/10}$, then, $(a^{2m+n-p})^2/(a^{m-2n+2p})^{-1} = ?$

If A={1, 2, 3, ... , 10}, then how many subsets of A contain the element 1, but not 4?

If a pole is 6 meters high and casts a shadow $2\sqrt{3}$ meters long on the ground, then the sun's elevation is

If the HCF of two natural numbers is 12 and the product of the numbers is 2028, how many such pairs exist?

Say for positive quantities a, b, $a + b$ equals $a^2 + ab + b^2$. Choose the nearest value to b if a is given as 0.5.

The value of q that satisfies $3^p + 5^q = 52$ and $3^{p-1} + 5^{q-1} = 14$ will be

A pyramid rises 'h' cm from a square base of side 'a' cm to a ridge parallel to one of the base's sides, and is the same length too. What is 'h' if the volume of the pyramid is half of that of a cube of side 'a'?

The ratio of alcohol to water in a vessel of capacity 80 litres is 5:3, and two draws of 20 litres each are planned. After the $1^{st}$ draw, 20 litres of water are poured into the vessel, mixed well, and then the $2^{nd}$ draw ensues. The liquid drawn in 2 lots is also mixed well in another vessel. What's the ratio of alcohol to water in this second vessel?

What is the condition for $x^2 + (a + b)x + ab$, with a and b non-zero, to have real roots?

From the given figure, find the length of the major arc AB

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If the roots of the quadratic equation $3x^2 - 2x - 1= 0$ are the intercepts of a line, then the line can be

Three women Swati, Khyati and Tripti earn a monthly salary in the ratio 3:4:5. They also invest part of this salary regularly each month, in the ratio 3:5:6, spending the rest. If Tripti spends a monthly amount that is $3/4^{th}$ of her income, what's the ratio of the three women's monthly spending, in the same order as mentioned above?

A three-digit number is chosen at random. Find the probability that its hundreds digit, tens digit and units digit are consecutive integers in descending order

If the difference between a two-digit and the number obtained by reversing its digits is 27, then find the difference between the digits of the two-digit number.

A trader prints price-tags after having decided to sell his product at 25% profit over the cost price that his supplier has just informed. He later realises that a 10% GST would also be payable on the product sourced from the supplier. What is his profit now, in percent?

There are 56 runners and 40 musicians in a school. These students are arranged into groups for a performance, so that each group consists of only runners or musicians, and every group contains an equal number of students. Find the minimum number of groups in which all the students can be accommodated?

If points A(1,6), B(5,2) and C(12,9) are three of the vertices of the parallelogram ABCD, then the equation of diagonal BD will be

If the breadth of a rectangle is increased by 5 cms, its area is increased by 25 sq.cm. If the length is increased by 5 cms, its area increases by 20 sq.cm. Find the area of the rectangle in sq.cm.

A firm projects its revenue to rise 20% in each of the next 3 years. At the same time, it projects costs to rise 10% each year. If profit this past year was Rs 10Cr on revenue of Rs 100 Cr, what will be the accumulated profit at the end of the 3rd year?

When three coins are tossed simultaneously, what is the probability of getting exactly one tail?

If $\cos\alpha + \cos\beta + \cos\gamma = 3$, then $\cos^3\alpha + \cos^3\beta + \cos^3\gamma$ will be

Navin got 60% of the maximum marks in his college's exam for his batch but missed that year's 'Deans List' threshold by 60 marks. His batchmate Pravin scored 80% of the maximum, and this score was 40 marks more than the same threshold. What was that year's 'Deans List' threshold?

Three small metallic cubes whose edges are in the ratio 3 : 4 : 5 are melted to form a big cube with no material lost. If the diagonal of the cube so formed is 18 cm, then the total surface area of the smallest cube (in $cm^2$) is

The sum of deviations of 'n' observations about 25 is 25 and sum of deviations of the same 'n' observations about 35 is -15. Then the arithmetic mean of the observations is

If the perimeter of a circle changed from $4\pi$ to $8\pi$, then what is the change in its area?

If $\sqrt{2^n} = 1024$, then $3^{(n/4 - 4)}$ is = ?

In $\triangle ABC$, $\angle A = 90^{\circ}$, if $\tan C = \sqrt{3}$, then find the value of $\sin B + \cos C - \cos^2 B$

Two dice were rolled simultaneously. Find the probability that the sum of the numbers on them was a prime number.

In normal times, a vegetable exporter assumes that 20% of the produce sent in a container will perish by the end of the voyage to international markets, and he prices the sent vegetables at Rs 2L per ton to enjoy a 20% profit. Due to difficult shipping conditions now, he estimates that 50% of his produce inside the container will become unsellable, despite transport costs per container also increasing from Rs 2L to Rs 4L. If a container can store 10 tons of vegetables, what would be the new price he would ask (per ton) to retain his profit?

A country has 3 major economic sectors: agriculture, manufacturing and services - with their share of the country's Gross Domestic Product (GDP) being 40, 20 and 40 percent, respectively. Of these, services is growing at 10% per annum, whilst agriculture is growing at 4%. The GDP in aggregate is estimated to be growing at 6% yearly: what is the annual rate of growth of manufacturing in percent?

A foreign country reduces its import duty on an Indian exporter's product from 30% to 10%. The exporter estimates that the reduction in import duties - which he will pass on fully by reducing prices -- will increase the volume of sales by 50%. The revenue obtained in that market turned out to be Rs 165Cr. What would the revenue have been if the exporter continued selling at the old price?